Answer:
[tex]f'(x)=-8\sin2x+\frac{1}{x} +1[/tex]
Step-by-step explanation:
I assume by [tex]\log(x)[/tex], the base is [tex]e[/tex], so let [tex]\log_e(x)=\ln(x)[/tex]:
[tex]\displaystyle f(x)=4\cos2x+\ln x+x\\\\f'(x)=\frac{d}{dx}(4\cos2x+\ln x + x)\\\\f'(x)=\frac{d}{dx}(4\cos2x)+\frac{d}{dx}(\ln x)+\frac{d}{dx}(x)\\\\f'(x)=-8\sin2x+\frac{1}{x}+1[/tex]
Remember that by the chain rule, to find the derivative of [tex]4\cos2x[/tex], you must find the derivative of the inside, which is [tex]\displaystyle \frac{d}{dx}(2x)=2[/tex], and multiply it by the outside derivative. Recall that [tex]\displaystyle \frac{d}{dx}\cos(x)=-\sin(x)[/tex], so replace [tex]-\sin(x)[/tex] with [tex]-4\sin(2x)[/tex], and multiply by 2 to get [tex]-8\sin(2x)[/tex] as your derivative.
Also remember that [tex]\displaystyle \frac{d}{dx}\ln(x)=\frac{1}{x}[/tex], one of the more basic derivatives.
The derivative of the function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given function is four times of cos2x plus logx plus x.
f(x)= 4cos2x + logx + x
We need to find the derivative of it f'(x)
d/dxf(x)=d/dx(4cos2x)+d/dx(logx)+d/dx(x)
f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)
We know that
d/dx(cosx)=-sinx
d/dx(logx)=1/x
d/dx(x)=1
Apply in above equation
f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)
f'(x)=4.2(-sin2x)+1/x+1
f'(x)=-8sin2x+1/x+1
Hence the derivative of function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.
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Which of the following polynomial functions is graphed below?
-70
60
50
20
-10
O A. f(x) = (x + 5)(x − 1)2(x+1)
B. f(x) = (x - 5)(x-1)²(x - 1)
OC. f(x) = (x+2)(x-3)²(x+4)
D. f(x)=(x-2)²(x-3)(x-4)
-10-
-20
-30-
-40
10
The option (C) f(x) = (x+2)(x-3)²(x+4) is correct because in the graph the minimum value of function is less than 40.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a graph of a polynomial.
From the graph we can clearly see there is three x-intercept where the value of a polynomial function becomes zero.
The minimum value of function is less than 40
At x = 3, f(3) = 0
At x = -2, f(-2) = 0
At x = -4, f(-4) = 0
Thu graph of a function will be:
[tex]\rm y\ =\ \left(x+2\right)\left(x-3\right)^{2}\left(x+4\right)[/tex]
Thus, the option (C) f(x) = (x+2)(x-3)²(x+4) is correct because in the graph the minimum value of function is less than 40.
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Which of these need to be purchased in addition to renter's insurance? Select all that apply.
-Earthquake insurance
-fire insurance
-flood insurance
-Lightning insurance
-tornado insurance
The following needs to be purchased in addition to renter's insurance;
Earthquake insuranceflood insurancetornado insurance What is renters insurance?Renter’s insurance is a policy which covers the loss of people renting or subletting a property. It helps to protect against loss of properties within the insured apartment.
Here are some problems covered by renters insurance:
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Drag each tile to the correct box.
Each tile shows an investor’s tax bracket along with the tax-free yield of a bond the investor purchased. Use the formula to determine the taxable equivalent yield of each investment, and then order the investments from least to greatest return.
taxable equivalent yield =
100 PTS
The order the investments from least to greatest return,
tax bracket is 22% and tax-free yield is 3% < tax bracket is 35% and tax-free yield is 3% < tax bracket is 24% and tax-free yield is 4% < tax bracket is 12% and tax-free yield is 5% < tax bracket is 12% and tax-free yield is 5%
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
We know the value of a fraction gets larger when the numerator becomes larger and the denominator gets smaller.
Given, Each tile shows an investor’s tax bracket along with the tax-free yield of a bond the investor purchased.
(tax-free yield)/(100 - tax bracket).
Now, tax bracket is 24% and tax-free yield is 5%.
= 5/100 - 24.
= 5/76.
= 0.0658.
Similarly,
tax bracket is 12% and tax-free yield is 5%
= 0.0641.
tax bracket is 22% and tax-free yield is 3%
= 0.0384.
tax bracket is 24% and tax-free yield is 4%
= 0.0526.
tax bracket is 35% and tax-free yield is 3%
= 0.0461.
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2. Given the following angle measurements for a triangle, find the remaining angle.
a. 53, 69
b. 105, 47
c. 90, 25
Write the following phrase as an algebraic expression. Use x for the unknown number.
The sum of -8 and four times a number.
Work Shown:
x = unknown number
4x = four times the unknown number
-8+4x = sum of -8 and the previous expression
-8+4x is the same as 4x+(-8) or 4x-8
Given that the quadrilateral is a parallelogram, find the values of x, y and z.
Answer:
x=9
y=4
z=4
Step-by-step explanation:
9x-13=7x+5
9x-7x=5+13
2x=18
x=18/2=9
3y=12
y=12/3=4
11z-41=5z-17
11z-5z=-17+41
6z=24
z=24/6=4
Which is the graph of 5 log (x + 3)?
Graph is in attached image.
Katherine wants to use a sheet of fiberboard 18 inches long to create a skateboard ramp with a 17
∘
∘
angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary.
The rise from the ground by the skateboard is 5.5 inches
How to determine the height above the ground?The length of the skateboard is given as:
Length (l) = 18 inches
The angle of elevation (x) is
x = 17∘
Represent the height with h.
The value of h is calculated using the following tangent ratio:
tan(x) = h/l
Make h the subject
h = l * tan(x)
Substitute known values
h = 18 * tan(17)
Evaluate
h = 5.5
Hence, the rise from the ground by the skateboard is 5.5 inches
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Answer: 5.3
Step-by-step explanation:
SOH-CAH-TOAsin 17=oppositehypotenuse=x18sin 17=hypotenuseopposite=18xsin 17=sin 17= x1818xsin 171=1sin 17= x1818x18 sin 17=18 sin 17= xxx=5.262690...≈5.3x=5.262690...≈5.3
What are the solutions for the following system of equations?
3x² + 4y - 21
4x² + y = 10
(1,6) and (0, 10)
(-1,6) and (1. 6)
(1,6) and (3, 12) G1
(-1, 6) and (3. 12)
We will use graphical way to solve these
3x²+4y-21=04x²+y=10Graph both
The solutions are
(±1.209,4.154)None of the above
A set of cards contains the numbers 1 through 20. Mathieu chooses a card at random, records the number of the card, and then returns the card to the set. He conducts 200 trials of this event. Based on the theoretical probability, how many times can Mathieu expect to choose a multiple of 5?
10
20
40
50
Answer:
20
Step-by-step explanation:
Answer:
the one above me is WRONG, its 40 i swear i just did the unit test
Step-by-step explanation:
What is the degree of the polynomial 6x^2+x^9+5x^7+20x^6
The degree of a polynomial is the highest exponent of the algebraic expression.
[tex]6 {x}^{2} \: + \: {x}^{ \boxed{ \bold{9}}} \: + \: 5 {x}^{7} \: + \: 20 {x}^{6} [/tex]
R// The degree of the polynomial is 9MissSpanishWhich statement best compares savings accounts and money market accounts?
OA. A regular savings account has fewer restrictions on withdrawals than a money market account
but at a lower interest rate.
OB. A regular savings account has fewer restrictions on withdrawals than a money market account
but at a higher interest rate.
C. A money market account has fewer restrictions on withdrawals than a regular savings account
but at a lower interest rate.
OD. A money market account allows for more withdrawals than a regular savings account but at a
higher interest rate.
Answer:
Its Option C.
Step-by-step explanation:
I took this quiz and got this correct, atleast I think...??
Lin surveyed a class of sixth-graders asking how many hours they spend online every month.
They spend about three hours a day online
The perimeter of this square is 24x – 20. Which expression represents the length of a side?
6x – 5
12x – 5
4x – 4
Answer:
6x-5
Step-by-step explanation:
We have to find 2 sides added together, so we do (24x-20)/2=12x-10. (12x-10)/2=6x-5, so it is 6x-5.
if x=2, and y=-3, then xy^2 =
Answer:
36
Step-by-step explanation:
If x = 2 and y = -3...
xy^2=
(2)(-3)^2 =
-6^2 =
36
XY times 2=
(-6)(2) =
-12
Answer:
18
Step-by-step explanation:
First you must fill input the values into their variable counterparts:
xy^2 turns into: 2 * -3 ^2
Since there isn't a parenthesis around x AND y, the exponent only applies to the y value.
-3 ^2 = 9, so 2 x 9 = 18
xy^2 = 18 if x =2 and y = -3
( -16 + 12 ) ÷ ( -4 + 2 ) = What is the Answer
Find out the sum by suitable arrangement.
1 + 2 + 3 + 4 + 5 + 95 + 96 + 97 + 98 + 99
1 + 2 + 3 + 4 + 5 + 95 + 96 + 97 + 98 + 99. = 500
Answer:
500
Step-by-step explanation:
rearrange the sum as
(99 + 1) + (98 + 2) + (97 + 3) + (96 + 4) + (95 + 5)
= 100 + 100 + 100 + 1000 + 100
= 5 × 100
= 500
The point at which three or more lines intersect is the point of _____ concurrency. concurrency. tangency. equality. parallelism.
The point at which three or more lines intersect is the point of concurrency.
What is the point where three line intersect?The point were three lines meet or intersect is a point of concurrency.
In other words, a point of concurrency is where three or more lines intersect in one place.
This point of concurrency is a single point shared by three or more lines.
Perpendicular bisectors, and altitudes are concurrent in every triangle.
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Answer:
concurrency
Step-by-step explanation:
Look above for more
the sum of 6 and the product of 8 and x
Answer:
6+8x
Step-by-step explanation:
.Find the distance between the two points
(3, 5) and (4, 6) to the nearest tenth.
7 x 3 1/4 = in fraction
Answer:
22 3/4
Step-by-step explanation:
divide 1/4 which is 0.25, then add 3 to that, then multiply it by 7 which is 22.75
then convert it back into a fraction which is 22 3/4
Please help! photo is attached, will give brainliest.
Answer:84
Step-by-step explanation:
Okay. Are you taking calc? Dv/dt =d/dt(L(t)^3)=d/dt[(sqrt(14)+2t)^3]= 6(Sqrt(14)+2t)^2)=44. We defined t=0 to be time at which length is sqrt(14). Does that work?
What is the volume of the following solid figure?
Answer: 450
Step-by-step explanation:
The volume is (1/2)(5)(12)(15)=450.
Tricia is going too write patterns a, b, and c using the rule "add 15." the first number in each pattern is shown below. Use the drop-down menus too describe the patterns. Pattern A: 5
Pattern B: 10
Pattern C: 15
Each patter will blank
A: contain odd numbers only
B: alternate between odd and even numbers
C: Include a number with 2 in the ones place
D: Include a number with 1 in the tens place
Answer:
Number 40 appeared in Pattern B. Also, according to the rule, each pattern will increase.
Step-by-step explanation:
Let's develop each sequence. Remembe that the rule is "add 15", that's what we need to create each sequence starting from the given initial number.
Pattern A.

Pattern B.

Pattern C.

As you can observe, number 40 appeared in Pattern B. Also, according to the rule, each pattern will increase
What is true about AngleQRT? Select two options.
Measure of angleQRT = 90°
Measure of angleQRT = Measure of angleSRT
AngleQRT Is-congruent-to AngleSTQ
Measure of angleQRT = 2*Measure of angleRTQ
AngleQRT Is-congruent-to AngleRTQ
The complete question is
"Triangle QST is isosceles, and Line segment R T bisects AngleT. Triangle Q S T is cut by bisector R T. The lengths of sides S T and Q T are congruent. Line segments S R and R Q are congruent. Angles S T R and R T Q are congruent. What is true about AngleQRT?
Select two options. Measure of angleQRT = 90° Measure of angleQRT = Measure of angleSRT AngleQRT Is-congruent-to AngleSTQ Measure of angleQRT = 2*Measure of angleRTQ AngleQRT Is-congruent-to AngleRTQ"
The true about AngleQRT options are A abd B; ∠QRT = 90 and ∠QRT = ∠SRT
What is the congruent triangle?Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.
Given information;
The triangle QST is isosceles with QT ≅ ST.
The ∠STR and ∠RTQ are congruent.
Now, consider two triangles ∠QTR and ∠STR
In the following triangle
TR ≅ TR
QTR ≅ STR
QT ≅ ST
Now, according to SAS rule, two congruent triangles have congruent corresponding to their sides,
1. QR ≅ SR
2. QRT ≅ SRT
Since the above two angles are congruent so, they will have the same measure
That will be 90 degree.
Hence, The correct options are; ∠QRT = 90 and ∠QRT = ∠SRT
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If a sample proportion is 0.65, which range of possible values best describes
an estimate for the population parameter?
O A. (0.5, 0.89)
• B. (0.5, 0.8)
• C. (0.65, 0.7)
• D. (0.6, 0.69)
The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8)
How to estimate proportion?The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8).
When we are talking about population parameters, we also have to look at the way of estimating the population, we have to add two extremes and divide by 2.
Thus, the correct one is;
(0.5 + 0.8)/2 = 0.65
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Part 3 - Discussion/Explanation Question
In what ways can vertical, horizontal, and oblique asymptotes be identified? Use a mathematical example to
explain the ways.
Step-by-step explanation:
Vertical asymptote can be Identites if there is a factor only in the denominator. This means that the function will be infinitely discounted at that point.
For example,
[tex] \frac{1}{x - 5} [/tex]
Set the expression in the denominator equal to 0, because you can't divide by 0.
[tex]x - 5 = 0[/tex]
[tex]x = 5[/tex]
So the vertical asymptote is x=5.
Disclaimer if you see something like this
[tex] \frac{(x - 5)(x + 3)}{(x - 5)} [/tex]
x=5 won't be a vertical asymptote, it will be a hole because it in the numerator and denominator.
Horizontal:
If we have a function like this
[tex] \frac{1}{x} [/tex]
We can determine what happens to the y values as x gets bigger, as x gets bigger, we will get smaller answers for y values. The y values will get closer to 0 but never reach it.
Remember a constant can be represent by
[tex]a \times {x}^{0} [/tex]
For example,
[tex]1 = 1 \times {x}^{0} [/tex]
[tex]2 = 2 \times {x}^{0} [/tex]
And so on,
and
[tex]x = {x}^{1} [/tex]
So our equation is basically
[tex] \frac{1 \times {x}^{0} }{ {x}^{1} } [/tex]
Look at the degrees, since the numerator has a smaller degree than the denominator, the denominator will grow larger than the numerator as x gets larger, so since the larger number is the denominator, our y values will approach 0.
So anytime, the degree of the numerator < denominator, the horizontal asymptote is x=0.
Consider the function
[tex] \frac{3 {x}^{2} }{ {x}^{2} + 1} [/tex]
As x get larger, the only thing that will matter will be the leading coefficient of the leading degree term. So as x approach infinity and negative infinity, the horizontal asymptote will the numerator of the leading coefficient/ the leading coefficient of the denominator
So in this case,
[tex]x = \frac{3}{1} [/tex]
Finally, if the numerator has a greater degree than denominator, the value of horizontal asymptote will be larger and larger such there would be no horizontal asymptote instead of a oblique asymptote.
Select the correct answer.
An airline operates in only 10 destinations in 2015, but plan on adding more destinations each year. In 2016, the number of destinations will be
twice the initial number of destinations. Then, in 2017, the number of destinations will be twice the number of destinations the previous year. If
this pattern continues, which of the following graphs represents the number of destinations in which the airline will operate over time?
Answer:
would need to see the graph
Step-by-step explanation:
see answer advice
What is 3.9443.9443, point, 944 rounded to the nearest hundredth?
Answer:
3.94
Step-by-step explanation:
3.944 rounded to nearest hundredth = 3.94 becuase the thousandth digit is <5 you do not change the hundredth
a flower garden is in the shape of a circle. The circumfrence of the garden is 20 meters. What is the area of the garden? use 3.14 for pie and round your answer to the nearest whole number
Answer:
32m²
Step-by-step explanation:
r=
[tex] \frac{c}{2\pi } [/tex]
r=20/(2×3.14)= 3.18m
A=pi r² = 3.14x3. 18² = 32m²